{"paper":{"title":"Rational Mode Locking for Homeomorphisms of the 2-Torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Patrice Le Calvez, Salvador Addas-Zanata","submitted_at":"2015-08-11T13:59:41Z","abstract_excerpt":"Let $f:{\\rm T^2\\rightarrow T^2}$ be a homeomorphism homotopic to the identity, $\\widetilde{f}:{\\rm I}\\negthinspace {\\rm R^2\\rightarrow I} \\negthinspace {\\rm R^2}$ be a fixed lift and $\\rho (\\widetilde{f})$ be its rotation set, which we assume to have interior. We also assume that some rational point $(\\frac pq,\\frac rq)\\in \\partial \\rho (\\widetilde{f})$ and we want to understand how stable this situation is. To be more precise, we want to know if it is possible to find two different homeomorphisms, which are arbitrarily small $C^0$-perturbations of $f,$ denoted $f_1$ and $f_2,$ in a way that $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02597","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}